Abstract

Matching minors are a specialised version of minors fit for the study of graphs with perfect matchings. The first major appearance of matching minors was in a result by Little who showed that a bipartite graph is Pfaffian if and only if it does not contain \(K_{3,3}\) as a matching minor. Later it was shown, that \(K_{3,3}\)-matching minor free bipartite graphs are essentially, that is after some clean-up and with a single exception, bipartite planar graphs glued together at 4-cycles.

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